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A279767 Numbers n such that n and n + 2 have the same prime signature. 2
3, 5, 11, 17, 18, 29, 33, 41, 50, 54, 55, 59, 71, 85, 91, 93, 101, 107, 137, 141, 143, 149, 159, 179, 183, 185, 191, 197, 201, 203, 213, 215, 217, 219, 227, 235, 239, 242, 247, 248, 265, 269, 281, 299, 301, 303, 306, 311, 319, 321, 327, 339, 340, 347, 348, 391, 393, 411, 413 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence contains some terms such that n and n + 2k (1 < k) have the same prime signature.  For some terms where n and n + 2k share the same prime signature this means that every alternate element between, and including n and n + 2k have the same prime signature. The first such example is where a(41951)=402677, a(41953)=402679, and a(41955)=402681, share the same prime signature {1, 1}. Also the remaining alternate terms excluding endpoints share the same prime signature. Using the above example a(41952)=402678 and a(41954)=402680, share the prime signature {1,1,3}. - Torlach Rush, Feb 25 2018

LINKS

Michel Marcus, Table of n, a(n) for n = 1..5585

Index to sequences related to prime signature

EXAMPLE

18 is a term because 18 = 2 * 3^2 and 18 + 2 = 20 = 2^2 * 5.

19 is not a term because it is prime and 21 is the product of two primes, so the prime signatures are different.

MATHEMATICA

primeSignature[n_] := Sort[Transpose[FactorInteger[n]][[2]]]; Select[ Range[2, 1000], primeSignature[#] == primeSignature[# + 2] &] (* Adapted from A052213 *)

PROG

(PARI) isok(n) = vecsort(factor(n)[, 2]) == vecsort(factor(n+2)[, 2]); \\ Michel Marcus, Feb 25 2018

CROSSREFS

Cf. A001359, A052213, A052214.

Sequence in context: A323582 A088328 A102643 * A125631 A045408 A092740

Adjacent sequences:  A279764 A279765 A279766 * A279768 A279769 A279770

KEYWORD

nonn,easy

AUTHOR

Altug Alkan, Dec 18 2016

STATUS

approved

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Last modified May 21 04:46 EDT 2022. Contains 353887 sequences. (Running on oeis4.)